Name
Abstract | ||
|---|---|---|
We present the first ratio-based image segmentation method that allows imposing curvature regularity of the region boundary. Our approach is a generalization of the ratio framework pioneered by Jermyn and Ishikawa so as to allow penalty functions that take into account the local curvature of the curve. The key idea is to cast the segmentation problem as one of finding cyclic paths of minimal ratio in a graph where each graph node represents a line segment. Among ratios whose discrete counterparts can be globally minimized with our approach, we focus in particular on the elastic ratio [Formula: see text] that depends, given an image I, on the oriented boundary C of the segmented region candidate. Minimizing this ratio amounts to finding a curve, neither small nor too curvy, through which the brightness flux is maximal. We prove the existence of minimizers for this criterion among continuous curves with mild regularity assumptions. We also prove that the discrete minimizers provided by our graph-based algorithm converge, as the resolution increases, to continuous minimizers. In contrast to most existing segmentation methods with computable and meaningful, i.e., nondegenerate, global optima, the proposed approach is fully unsupervised in the sense that it does not require any kind of user input such as seed nodes. Numerical experiments demonstrate that curvature regularity allows substantial improvement of the quality of segmentations. Furthermore, our results allow drawing conclusions about global optima of a parameterization-independent version of the snakes functional: the proposed algorithm allows determining parameter values where the functional has a meaningful solution and simultaneously provides the corresponding global solution. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1109/TIP.2011.2118225 | IEEE Transactions on Image Processing |
Keywords | Field | DocType |
local curvature,corresponding global solutio,introducing curvature,existing segmentation method,ratio framework,mild regularity assumption,minimal ratio,ratio-based image,curvature regularity,ratio amount,elastic ratio,global optimum,minimization,optimization,polynomials,global optimization,edge detection,image segmentation,graph,computational modeling,image resolution,graph theory,computer model,penalty function,curvature,pixel | Graph theory,Line segment,Computer vision,Curvature,Polynomial,Global optimization,Segmentation,Image segmentation,Degeneracy (mathematics),Artificial intelligence,Mathematics | Journal |
Volume | Issue | ISSN |
20 | 9 | 1941-0042 |
Citations | PageRank | References |
16 | 0.59 | 42 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Thomas Schoenemann | 1 | 353 | 21.15 |
| Simon Masnou | 2 | 124 | 9.26 |
| Daniel Cremers | 3 | 8236 | 396.86 |